MIT OCW.
Sound and Hearing
Sound
ƒ vibrating medium
ƒ longitudinal wave
ƒ v=λxf
Vibrating body
(sound source)
Wavelength =
Amplitude
Image by MIT OCW.
Frequency = f
Wavelength =
Velocity of
propagation
v
Amplitude
Image by MIT OCW.
Sound and Hearing
Sound
ƒ pressure p in Pa
ƒ intensity I in W/m2
General relation: I = p2 / (ρ v)
For standard conditions: p = 20 √( I )
ƒ thresholds of audibility and pain (at 1000 Hz)
Io = 1 pW/m2 (i.e. 10-12 W/m2)
Ipain = 1 W/m2
po = 20 μPa = 2 10-5 Pa
ppain = 20 Pa
Sound and Hearing
Sound field
ƒ Point source
ƒ Cylindrical source
attenuation with distance
ƒ Large source
R2
L
R
L >> λ
R1
Sound and Hearing
Sound field
ƒ Obstacles
calculation of characteristic frequency f0
fo = d v / (2 H2)
Low frequency: diffraction
Straight Path
High frequency: acoustic shadow
Direct Sound
Image by MIT OCW.
Bright Zone
Shadow Zone
H
Diffracted Sound
d1
Barrier
source
d2
Reflected Sound
d = min(d1,d2)
Image by MIT OCW.
Receiver
Sound and Hearing
Hearing
ƒ logarithmic dependence of sensation on stimulus
2
Sensation
1.5
1
.5
0
0
20
40
60
80
100
Excitation (intensity)
Image by MIT OCW.
Sound and Hearing
Hearing
ƒ sound level L in dB
⎛ I
L = 10 Log ⎜⎜
⎝ Io
⎞
⎛ p ⎞
⎟⎟ = 20 Log ⎜⎜ ⎟⎟
⎠
⎝ po ⎠
Sound and Hearing
Hearing
ƒ sound level L in dB
ƒ contribution of two sounds to total sound level
Image by MIT OCW.
Sound and Hearing
120
ƒ dependence on frequency
100
80
60
40
20
0
10
100
1000
10000
Frequency (Hz)
Relative response (dB)
ƒ sound level L in dB
Intensity in decibels (dB)
Hearing
0
C
B and C
-10
A
B
-20
-30
A
-40
20
100
1000
Frequency (Hz)
10000
Images by MIT OCW.
Sound and Hearing
Hearing
ƒ Human ear
Semi-circular Canals
Pinna or
Auricle
Malleus
(Hammer)
Incus (Anvil)
Auditory
Nerve
Auditory Canal
Cochlea
io
ch
ta
e
b
Tu
Staples
(Stirrup)
us
E
Tympanic
Membrane
(Ear Drum)
o
(t
)
at
ro
th
Lobule
Image by MIT OCW.
Sound and Hearing
1
10-12
Audible sounds
Below threshold
sounds
20
Ultra sounds
ƒ Human ear
Super sounds
Infra sounds
Intensity (W/m2)
Hearing
Threshold of pain
Threshold of audibility
16,000
Frequency (Hz)
Reduction in threshold level: dB
0
Image by MIT OCW.
25 Hz
1 kHz
10
4 kHz
20
8 kHz
30
40
16 kHz
50
60
70
20
30
40
50
Age: years
60
70
Image by MIT OCW.
Sound and Hearing
Hearing
ƒ Human ear
ƒ Sound spectrum
1
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
0.5
0
-0.5
-1
0
2000
4000
0
1
6000
8000
2
3
10000
Image by MIT OCW.
Sound and Hearing
Hearing
ƒ Human ear
ƒ Sound spectrum
[ ]
1
Amplitude
0.8
0.6
0.4
0.2
0
10
Sound
Pure sound
Noise
100
1000
Frequency [Hz]
10000
Sound and Hearing
Noise level
Noise Level
Effect
150 dB
cause instant loss of hearing.
120 dB
is physically painful and should be avoided.
100 dB
short periods of exposure cause a temporary loss of
acuity (threshold shift) with prolonged exposure
likely to cause irreparable damage to auditory organs.
90 dB
long term exposure at this level normally causes
permanent hearing loss.
65 dB
long periods of exposure cause both mental and
bodily fatigue.
Image by MIT OCW.
Sound and Hearing
Noise level
In a bedroom
30 - 40 dBA
For intellectual work
50 - 70 dBA
For manual work
80 dBA
Sound and Hearing
Noise level
Perceived as:
Variation
Factor
Inaudible variation
1 dB
1,25
Barely audible
3 dB
2
Convincing
5 dB
3
10 dB
10
Twice as strong
Sound and Hearing
Reading assignment from Textbook:
ƒ “Introduction to Architectural Science” by Szokolay: § 3.1 - 3.2
Additional readings relevant to lecture topics:
ƒ "How Buildings Work" by Allen: pp. 124-129 in Chap 14